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Local spectrum and subharmonicity

Published online by Cambridge University Press:  20 January 2009

B. Aupetit  and
D. Drissi
B. Aupetit
Affiliation:
Départment de Mathématiques et de StatistiqueUniversité LavalQuébec QcCanadaG1K 7P4
D. Drissi
Affiliation:
Department of MathematicsFaculty of SciencesKuwait UniversityP.O. Box 5969 Safat 13060, Kuwait
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Abstract

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Introducing the technique of subharmonic functions, we prove that the local spectrum Spu(λ)(T) is almost constant if u is an analytic family of vectors and if the spectrum of T is thin, a result which is similar to the finite-dimensional situation. We apply this result to improve a former result of C. Foiaş [7] on generalized scalar operators and results of C. Foiaş and F. -H. Vasilescu [8] on generalized commutators.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 3 , October 1996 , pp. 571 - 579
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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